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Covering arrays are structures for well-representing extremely large input spaces and are used to efficiently implement blackbox testing for software and hardware. This paper proposes refinements over the In-Parameter-Order strategy (for arbitrary t). When constructing homogeneous-alphabet covering arrays, these refinements reduce runtime in nearly all(More)
We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing algorithms (PIT) for algebraic branching programs (ABPs) that are read-once and oblivious. This class has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka), but prior to this work there was no known such(More)
Mulmuley [Mul12a] recently gave an explicit version of Noether's Normalization lemma for ring of invariants of matrices under simultaneous conjugation, under the conjecture that there are deterministic black-box algorithms for polynomial identity testing (PIT). He argued that this gives evidence that constructing such algorithms for PIT is beyond current(More)
We give deterministic black-box polynomial identity testing algorithms for multilinear read-once oblivious algebraic branching programs (ROABPs), in <i>n</i><sup>O</sup>(log<sup>2</sup> <i>n</i>) time. Further, our algorithm is oblivious to the order of the variables. This is the first sub-exponential time algorithm for this model. Furthermore, our result(More)
Binary covering arrays of strength t are 0–1 matrices having the property that for each t columns and each of the possible 2 t sequences of t 0's and 1's, there exists a row having that sequence in that set of t columns. Covering arrays are an important tool in certain applications, for example, in software testing. In these applications, the number of(More)
Consider a possibly non-linear (n, K, d) q code. Coordinate i has locality r if its value is determined by some r other coordinates. A recent line of work obtained an optimal trade-off between information locality of codes and their redundancy. Further, for linear codes meeting this trade-off, structure theorems were derived. In this work we give a new(More)
We say that a circuit C over a field F functionally computes an n-variate polynomial P ∈ F[x 1 , x 2 ,. .. , x n ] if for every x ∈ {0, 1} n we have that C(x) = P(x). This is in contrast to syntactically computing P, when C ≡ P as formal polynomials. In this paper, we study the question of proving lower bounds for homogeneous depth-3 and depth-4 arithmetic(More)
The results of Strassen~\cite{strassen-tensor} and Raz~\cite{raz} show that good enough tensor rank lower bounds have implications for algebraic circuit/formula lower bounds. We explore tensor rank lower and upper bounds, focusing on explicit tensors. For odd d, we construct field-independent explicit 0/1 tensors T:[n]^d\to\mathbb{F} with rank at least(More)
We study the problem of obtaining efficient, deterministic, <i>black-box polynomial identity testing algorithms</i> for depth-3 set-multilinear circuits (over arbitrary fields). This class of circuits has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka [36]), but has no known such black-box algorithm. We(More)
Kayal has recently introduced the method of shifted partial derivatives as a way to give the first exponential lower bound for computing an explicit polynomial as a sum of powers of constant-degree polynomials. This method has garnered further attention because of the work of Gupta, Kamath, Kayal and Saptharishi who used this method to obtain lower bounds(More)